improvement power system dynamic stability by using upfc
TRANSCRIPT
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
Improvement Power System Dynamic Stability
by Using UPFC with Practical Constraints
M. Maleki rizi1; S. Abazari2,*; N. Mahdian3
1- Department of Engineering, Shahrekord University, Shahrekord, Iran.
2- Department of Engineering, Shahrekord University, Shahrekord, Iran, Email: [email protected]
3- Shahid Rajaie Teacher Training University, Tehran, Iran
*Corresponding Author
Received: 2020-07-26
Revised: 2020-12-15
Accepted: 2021-02-13
Abstract This paper presents enhancement of power system dynamic stability by using unified power flow controller with assuming several real conditions and practical power system constraints. In control method design, we used all four
UPFC basic controllers simultaneously with reducing conflict of them by compromising between its control variables.
Optimization problem have been used with regarding some constraints of the system and unified power flow controller.
Particle swarm optimization algorithm has used to optimize power oscillation damping based on unified power flow
controller with an objective function. Simulation results in several multi-machine test power systems demonstrate the
capability of applied control system with regarding many constraints and limits of power system and UPFC in different
scenarios.
Keywords: Dynamic stability, unified power flow controller, practical constraints, optimization, multi-machine power
system.
1. Introduction
Electric power demand increase, bounds the power
systems to stress conditions, and leads to undesirable
system parameters. To have secure operation of power
systems, damping of power system oscillations have
attracted a great deal of attention in power-system
stability studies. New FACTS devices can be effective in
controlling power flow and damping power system
oscillations and may use to increase power system
operation's flexibility and controllability, to enhance
system stability and to achieve better utilization of
existing power systems. UPFC is the most important and
comprehensive device and has capability of regulating
active and reactive power flow and stability improvement
in power system. UPFC consists of two converters
coupled through a common DC link large capacitor.
UPFC is able to control, selectively or simultaneously,
transmission network bus-voltage, line impendence or
alternatively, the real and reactive power flow in the line
by means of series voltage-vector injection. The UPFC
can also provide controllable shunt reactive
compensation independently. These duties fulfil with to
converter voltage magnitude and phase angle control that
commonly used PI control.
In inter-area modes, PSS may not produce enough
damping, But UPFC is as an interesting approach to help
to overcome several power system operating difficulties
and controlling voltages at critical buses, transient
stabilization and small signal and dynamic control and
consequently the overall stability of power systems [1].
UPFC employing a feedback supplementary controller
can not only considerably enhance system. It can enhance
damping effect in inter-area oscillations and thus these
are advantageous over PSSs [2]. Damping effect of
UPFC based POD with PSS have compared and better
result of UPFC based one is resulted too [3]. To
investigate UPFC damping effect, LQR and UPFC
control effects on dynamic stability improvement in
SMIB had compared [4]. A fuzzy method had used to
tune series inverter PI controllers in two-area power
system and tended to decrease in oscillation of active
power [5]. PSO technique have been used in two PI
tanning of UPFC in three-machine power system, to
reduce settling time too [6]. To UPFC POD controller
design in MMPS, in three-machine system, with
selecting damping ratio based objective function LQR
have used under different loading condition and better
result demonstrated [7]. Many researchers use PSO for
this application and some of them used adaptive PSO to
improve damping controller results in compare with
standard PSO and some other previous PSO types[1].
IGWO had compared with DE and PSO to optimize
UPFC POD controller with ITAE criteria too and
demonstrated stability enhancement of MMPS in three-
machine system while comparing using only 𝑚𝐵 or 𝛿𝐸
[8]. Several researches have tried to use improved
approaches of PSO to enhance oscillation damping of
power system such as [9], which try to optimize system
energy function using UPFC while only using two basic
controllers of UPFC in three-machine reduced power
system model. Already Comparison and Assessment of
Conventional and Optimal Coordinated PSS and UPFC
Damping Controller for SMIB system in SIMULINK
platform, regarding overshoot and settling time simulated
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
256
[10]. And stability enhancement of a three machine
system by using the coordinated application of the UPFC
and the PSS designed by using the Firefly algorithm and
was compared with Genetic search algorithm approach
too [11]. Synchronized use of PSS along with UPFC can
result in further improvement in reliability,
controllability and mitigation of power system
oscillations thus further improving the system stability.
using the evolutionary Cuckoo algorithm technique for
transient stability enhancement of two machine power
system, through coordinated design of SS and UPFC in
SIMULINK platform had examined too[12]. Recently
researchers, try to use some of nonlinear control methods
to control UPFC in single or multi machines power
system so in [13] we can see using multi input back
stepping in multi-machine power system equipped with
UPFC oscillation damping control.
In most previous researches to investigate UPFC
dynamic stability enhancement, they have not used all
basic controllers together and simultaneously and they
have not considered any practical limitation of power
network in these regulators adjustment too. If we don’t
consider the network limitations, it is possible that in
spite of achieving good damping and dynamic result, in
real condition we can’t use UPFC in those conditions,
because some limitations such as line thermal limits can
cause damage to system or instability in real conditions. Here, beside of using optimized POD controller with
Particle Swarm Optimization (PSO) algorithm, we have
used model of UPFC in multi-machine power system
(MMPS) to investigate dynamic stability with regarding
many constraints of power system such as line
transmission capacity limits in both steady state UPFC
calculations and small signal oscillations. Another
important constraint which we assumed while adjusting
power flow in line is rating limits of the UPFC because
in real condition the rating of devices and economic
conditions seriously limits these ratings. We will deal
with UPFC in the following section.
In many of those researches multi machine system only
simulated by SIMULINK and multi machine study
restricted only to three- machine or two-area system.
In the next section UPFC introduced. In section 3 and
4 basic control and supplementary control of UPFC
presented. After introducing PSO in section 5, in section
6 steady state and dynamic equations of power system
with UPFC installed described. Finally in section 7
results of this study demonstrated.
2. Unified power flow controller
The UPFC consists of a boosting transformer and an
excitation transformer linked by two back-to-back
converters. Figure 1 shows UPFC in power system.
Equation 1 expresses the UPFC terminals voltage
relation with dc link voltage and UPFC parameters.
��𝑬 =𝒎𝑬𝑽𝒅𝒄
𝟐𝒆𝒋𝜹𝑬 , ��𝑩 =
𝒎𝑩𝑽𝒅𝒄
𝟐𝒆𝒋𝜹𝑩 (1)
The series branch of the UPFC injects an AC voltage,
Where, mB is pulse width modulation of series
(boosting) converter. By 𝑚𝐵 controlling, the magnitude
of series injected voltage can be control. 𝑚𝐸 is pulse
width modulation of shunt (exciting) inverter. By 𝑚𝐸
controlling, the output voltage of the shunt converter is
controlling. 𝛿𝐵 is phase angle of series injected voltage.
𝛿𝐸 is voltage phase angle of the shunt inverter.
𝐾𝑤
𝑠𝑇𝑤
1 + 𝑠𝑇𝑤(1 + 𝑠𝑇1
1 + 𝑠𝑇2)(
1 + 𝑠𝑇3
1 + 𝑠𝑇4)
Fig. 1. UPFC in power system
with controllable magnitude and phase angle at the power
frequency [2]. And then can exchange real and reactive
power with installed line. The shunt converter has used
primarily to provide active power demand of the series
converter through a common DC link and can exchange
reactive power to adjust voltage of bus, which is
connected. Then UPFC is a combination of STATCOM
and SSSC.
The comprehensive models of UPFC for steady state,
transient stability and dynamic stability studies and also
dynamic model of the system installed with UPFC is
presented in [14]. Wang et al have proposed a unified
model of a multi-machine power system and developed
two UPFC models, which have been linearalized and
incorporated into the Phillips-Heffron model [14]. We
have used the comprehensive UPFC model, which is
more complete for steady state analysis and applicable in
power flow solution.
3. UPFC basic control
Figure 1 shows the UPFC power and control flow
diagram. As we can see, by adjusting the magnitude and
phase angle of the shunt (exciting) converter, bus voltage
and dc voltage across common capacitor will be
controlled. Shunt active and reactive power exchange is
related with active power which series converter request
and bus voltage requirements to be kept in accepted value
respectively. Active and reactive power flow can be
controlled by adjusting magnitude and phase angle of
series converter. Wang showed that parameters of UPFC
i.e. 𝒎𝑬 , 𝒎𝑩 , 𝜹𝑬 and 𝜹𝑩 should be modulated to
achieving desired damping of oscillation too. Equations
2 to 5 express these 4 basic control functions. Wang et al
investigated the control conflict between UPFC multiple
control functions and their interactions in single-machine
infinite -bus system and showed that sometimes using all
four control function may decrease accuracy of results
[15]. Then their adjustment with attention to this
interaction is very important. We used all of these four
controllers simultaneously and have done compromise
between four control variables.
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
257
𝜹𝑩 = (𝟏
𝟏+𝑻𝜹𝑩𝒔) (𝑲𝑷𝒑 +
𝑲𝑷𝒊
𝒔) (𝑷𝑹𝒆𝒇 − 𝑷) (2)
𝑚𝐵 = (1
1+𝑇𝑚𝐵𝑠) (𝐾𝑄𝑝 +
𝐾𝑄𝑖
𝑠) (𝑄𝑅𝑒𝑓 − 𝑄) (3)
𝑚𝐸 = (1
1+𝑇𝑚𝐸𝑠) (𝐾𝑉𝑝 +
𝐾𝑉𝑖
𝑠) (𝑉𝑅𝑒𝑓 − 𝑉) (4)
𝛿𝐸 = (1
1+𝑇𝛿𝐸𝑠) (𝐾𝐷𝐶𝑝 +
𝐾𝐷𝐶𝑖
𝑠) (𝑉𝐷𝐶,𝑅𝑒𝑓 − 𝑉𝐷𝐶) (5)
where 𝑻𝒙 are delay time constants, and 𝑲𝒙𝒑 and 𝑲𝒙𝒊 are
PI controllers proportional and integral gains
respectively. P, Q, V and 𝑽𝑫𝑪 are active and reactive
power flow through line and bus voltage which UPFC is
connected and UPFC dc link voltage respectively.
The main practical restriction that we want to apply to
system is real and reactive power limits which UPFC can
supply without any external power supply. Due to
technical and economic restriction the rating of UPFC
power is limited and this leads to applying limits of real
and reactive power by additional limiter blocks and then
modifying the UPFC related parameters in each iteration.
4. Power oscillation damping controller based on
UPFC
Secondary control design has known as the damping
controller design, which is a supplementary control loop
that is designed to enhance transient stability of entire
electric power system. The adverse interaction between
PSS and series part control have compensated by
providing UPFC based damping controller. Thus this is
another important reason of UPFC POD controller
improvement and its application beside basic controls.
Commonly the POD controllers have a transfer
function consisting of Gain, a washout function and two
lead-lag blocks. It is showed that the UPFC based POD
controller works effectively in single machine system. To
improve its dynamic performance in a multi-machine
system, the behaviour of the controllers must be
coordinated [16]. In [17] the speed deviation is selected
and all four parameters of UPFC tried to be output of
POD. And resulted that 𝒎𝑩is the best selection. In this
paper the active power of transmission line which UPFC
controls its power flow is used as input signal and we
have used this input and output. POD controller consists
of 𝑻𝑾 wash-out time constant which selected constant
and K wash-out gain and 𝑻𝟏to 𝑻𝟒 lead-lag time constants
which should be adjust.
Fixed parameter classical controller is not suitable for
the UPFC damping control design. Then, a flexible
controller should develop. Several approaches proposed
for it, such as root locus and sensitivity analysis, pole
placement, and robust control. The conventional
techniques require heavy computation and slow
convergence. And the search methods may be trapped in
local minimum and the solution obtained may not be
optimum. In addition, it is necessary that the designed
controller provide some robustness to the variations of
parameters, conditions, and configurations. Also the
controller parameters which stabilize the system in a
certain operating condition may no longer have
acceptable results in case of large disturbances [17].
We can use an optimization problem, base on Eigen
values multi-objective function reflecting the
combination of damping factor and damping ratio is
considered as:
𝐽 = ∑ ∑ (𝜎0 − 𝜎𝑖𝑗)2
𝜎𝑖≥𝜎0
𝑁𝑃
𝑗=1
+ 𝛼 ∑ ∑ (0
− 𝑖𝑗
)2
𝑖≥0
𝑁𝑃
𝑗=1
𝒇(𝒙) = 𝐦𝐢𝐧 𝑱
max
44
min
4
max
33
min
3
max
22
min
2
max
11
min
1
maxmin
TTT
TTT
TTT
TTT
KKK
(6)
where 𝝈𝒊𝒋 are real parts of system Eigen values and 𝝈𝟎 is
desired real part of Eigen value, 𝒊𝒋
are damping ratios of
system variables and 𝟎 is desired damping ratio. Both
real part and damping ratio are important in system
stability then the objective function consists of two parts
which each part related to each of these two main factors
and α is the constant coefficient which determine the
importance weight of the two parts of the objective
function. This optimization problem can solve with one
of analytical or numerical techniques. Here we have used
PSO which introduced briefly in next section.
5. Particle swarm optimization algorithm
PSO is an optimization technique which is population-
based introduced by Kennedy and Eberhart to solve the
optimization problem with constraint. In PSO system,
multiple solutions are candidate and collaborate
simultaneously. Each candidate, called a particle, flies in
the problem search space looking to land on the optimal
position. Particles, during the generations, adjusts their
own positions according to theirs own experience and the
experience of neighbour particles. This algorithm
combines global and local search methods, and tries to
balance exploitation and exploration. In this technique
new velocity and position of each particle will be updated
according to the following equations [18]:
NikXkgbestrc
kXkpbestrckVwkV
i
iiii
,,2,1,
1
22
11
(7)
11 kVkXkX iii
(8)
where N is number of particles, k is the current iteration,
𝒘 is an inertia weight, 𝒓𝟏 and 𝒓𝟐 are random variables
between 0 and 1, 𝒄𝟏 and 𝒄𝟐are acceleration coefficients.
𝑽𝒊 and 𝑿𝒊are the velocity and position of the particle 𝒊
respectively. 𝒑𝒃𝒆𝒔𝒕𝒊 is the local best position of particle 𝒊. gbest is the global- best position of all particles.
To optimize J function that mentioned above with PSO
the lead-lag controller parameters; 𝑻𝟏 to 𝑻𝟒 and wash-
out gain K are adjusted. The UPFC modeling together
with power system have dealt in next section.
6. Modelling and control of power system with
UPFC installed
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
258
Figure 2 shows the UPFC in multi-machine power
system. Performance analysis and control functions
synthesis of UPFC require its steady state and dynamic
models. In order to simulate the multi-machine power
system that contains a UPFC, the UPFC have modelled
for both steady state and dynamic operations condition.
Fig. 2. UPFC in multi-machine power system
6.1. Power system with UPFC steady state model
The basic control strategy is such that the shunt
converter of the UPFC controls the UPFC bus voltage,
shunt reactive power and the dc link capacitor voltage.
The series converter controls the transmission line real
and reactive power flow. Then the steady state model
assumes that the UPFC is operating to keep real and
reactive power flows at the receiving bus and to regulate
sending bus voltage magnitude. Thus a two-source UPFC
steady-state model including source impedances has
proposed in [19].
This UPFC model is extension of the power flow
equations and, hence, it is suitable for incorporation into
an existing Newton-Raphson load flow algorithm. In this
unified solution, the UPFC state variables have adjusted
simultaneously with the nodal network state variables.
Hence, the interaction between the network and the
UPFC has taken in to account.
These steady state parameters values will use to
calculate and determine base values of UPFC control
parameters. This load flow implementation can help to
select proper placement of UPFC.
With reducing bus admittance matrices to generator
internal buses and UPFC terminal bus the following
equation can be write:
U
G
U
G
UUUG
GUGG
I
II
V
EE
YY
YYY ,,
, ���� = ��
(9)
While, 𝒀𝑮𝑮 is reduced admittance matrices connecting
the generator current injection to the internal generator
voltages. 𝒀𝑮𝑼 is admittance matrices component which
gives the generator currents due to the voltages at UPFC
buses. 𝒀𝑼𝑮 is admittance matrices component which
gives UPFC currents in terms of the generator internal
voltages. 𝒀𝑼𝑼 is admittance matrices connecting UPFC
currents to the voltages at UPFC buses.��𝑮 is vector of
generator internal bus voltages. ��𝑼 is vector of UPFC ac
bus voltages. ��𝑮 is vector of generator current
injections. ��𝑼 is vector of UPFC currents injected to the
power network. Then, these parameters instant values
will incorporate in deriving matrices equation of multi
machine power system with UPFC installed which is
essential in dynamic stability analysis.
6.2. Power system linearzed model
Traditionally, for the small signal stability studies of
power system, the linear model of Phillips-Heffron has
used, and has provides reliable results [20]. Although the
model is linearized, it is enough accurate for studying low
frequency oscillations and dynamic stability of power
systems. The dynamic model of the system completely
presented in [20]. The injection model has used to
dynamic stability control of UPFC in MMPS modelling
too [4]. The nonlinear dynamic model of the system
installed with UPFC has given as (10)-(14). Equation (14)
shows the UPFC dynamics.
��𝑖 = 𝜔𝑏(𝜔𝑖 − 1)
(10)
ωi =(Pmi−Pei−Diωi)
Mi
(11) Eqi
′ =(−Eqi
′ +Efdi)
Tdoi′
(12)
Efdi =(−Efdi−Kai(VRef−Vt))
Tai
(13)
��𝐃𝐂 =𝟑𝐦𝐄
𝟒𝐂𝐝𝐜(𝐬𝐢𝐧𝛅𝐄𝐈𝐄𝐝 + 𝐜𝐨𝐬𝛅𝐄𝐈𝐄𝐪) +
𝟑𝐦𝐁
𝟒𝐂𝐝𝐜(𝐬𝐢𝐧𝛅𝐁𝐈𝐁𝐝 +
𝐜𝐨𝐬𝛅𝐁𝐈𝐁𝐪
(14)
where, i=1, 2, 3,…, n (the generators 1 to n), 𝜹𝒊 is rotor
angle of ith generator, 𝝎𝒊 is rotor speed of ith generator,
𝑷𝒎𝒊 is mechanical input power of ith generator, 𝑷𝒆𝒊 is
electrical output power of ith generator, 𝑬𝒒𝒊′ is internal
voltage behind 𝒙′ of ith generator, 𝑬𝒇𝒅𝒊 is equivalent
excitation voltage of ith generator, 𝑻𝒆𝒊 is electric torque
of ith generator, 𝑻𝒅𝒐𝒊′ is time constant of excitation circuit
of ith generator, 𝑲𝒂𝒊is regulator gain of ith generator, 𝑻𝒂𝒊
is regulator time constant of ith generator, is 𝑽𝒕𝑹𝒆𝒇𝒊 is
reference voltage of ith generator and 𝑽𝒕 is terminal
voltage. And:
𝑃𝑒 = 𝑉𝑇𝐷𝐼𝑑 + 𝑉𝑇𝑄𝐼𝑞 (15)
𝑉𝑇𝐷 = 𝑋𝑄𝐼𝑞 (16)
𝑉𝑇𝑄 = 𝐸𝑞′ − 𝑋𝐷
′𝐼𝑑 (17)
𝑉𝑇𝑖 = √𝑉𝑇𝐷𝑖2 + 𝑉𝑇𝑄𝑖
2 (18)
Where:
𝝎 = [ 𝜔1 𝜔2 … 𝜔𝑛]𝑇, 𝑬𝒒′ = [ 𝐸𝑞1
′ 𝐸𝑞2′ … 𝐸𝑞𝑛
′ ]𝑇
𝑬𝒇𝒅 = [ 𝐸𝑓𝑑1 𝐸𝑓𝑑2 … 𝐸𝑓𝑑𝑛]𝑇
𝑽𝑻𝒅 = [ 𝑉𝑑1 𝑉𝑑2 … 𝑉𝑑𝑛]𝑇 ,𝑽𝑻𝒒 = [ 𝑉𝑞1 𝑉𝑞2 … 𝑉𝑞𝑛]𝑇
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
259
𝑴 = 𝑑𝑖𝑎𝑔(2𝐻𝑖) , 𝑫 = 𝑑𝑖𝑎𝑔(𝐷𝑖)
𝑻𝒅𝒐′ = 𝑑𝑖𝑎𝑔(𝑇𝑑𝑜𝑖
′ ) , 𝑿𝑫 = 𝑑𝑖𝑎𝑔(𝐷𝑑𝑖)
𝑰𝒅 = [ 𝐼𝑑1 𝐼𝑑2 … 𝐼𝑑𝑛]𝑇 , 𝑰𝒒 = [ 𝐼𝑞1 𝐼𝑞2 … 𝐼𝑞𝑛]𝑇
𝐼�� = 𝐼𝑑𝑖 + 𝑗𝐼𝑞𝑖 (19)
ikik j
qkdkqk
j
qi
n
k
iki eIXXeEYI
)()2/(
1
(20)
As we can see in (9), Y is reduced admittance matrices
which contain only generators and UPFC buses. These
reduced admittance and consequently above mentioned
generators and UPFC currents represent all system power
flow. Another important practical constraint which we
have considered are limit of line thermal capacity which
can be limited by applying limits of line (𝑺𝒍𝒊𝒏𝒆,𝒍 ≤ 𝑺𝒎𝒂𝒙,𝒍 ,
𝒍 = 𝟏: 𝒏𝒍𝒊𝒏𝒆). While in each every iteration we compute
admittances, currents and powers. While we adjusting
UPFC parameters with considering these lines power
limits, we modify adjusted UPFC parameters.
Above equations can be rewritten in following matrices
form:
�� = 𝜔𝑏(𝛚 − 1) (21)
�� = 𝐌−1(𝐓𝐦 − 𝐓𝐞 − 𝐃(𝛚 − 1)) (22)
��𝐪′ = 𝐓𝐝𝐨
′ (𝐄𝐟𝐝 − 𝐄𝐪′ + (𝐗𝐝 − 𝐗𝐝
′ )𝐈𝐝) (23)
��𝐟𝐝 = (𝐊𝐀(𝐕𝐑𝐞𝐟 − 𝐕𝐭) − 𝐄𝐟𝐝)/𝐓𝐀 (24)
𝐓𝐞 = 𝐕𝐭𝐝𝐈𝐝 + 𝐕𝐐𝐈𝐭𝐪 (25)
𝑽𝒕𝒅 = 𝑿𝒒𝑰𝒒 , 𝑽𝒕𝒒 = 𝑬𝒒′ − 𝑿𝒅
′ 𝑰𝒅 (26)
With linearization above equations:
∆�� = 𝛚𝐛∆𝛚 (27)
∆�� = −𝐌−𝟏(∆𝐓𝐞 + 𝐃∆𝛚) (28)
∆��𝐪′ = 𝐓𝐝𝐨
′−𝟏(∆𝐄𝐟𝐝 − ∆𝐄𝐪′ + (𝐗𝐝 − 𝐗𝐝
′ )∆𝐈𝐝) (29)
∆��𝐟𝐝 = (𝐊𝐀(∆𝐕𝐫𝐞𝐟 − ∆𝐕𝐭) − ∆𝐄𝐟𝐝)𝐓𝐀−𝟏 (30)
∆𝐓𝐞 = ∆𝐈𝐪𝐄𝐪𝟎′ + 𝐈𝐪𝟎∆𝐄𝐪
′ + ∆𝐈𝐪(𝐗𝐪 − 𝐗𝐝′ )𝐈𝐝𝟎 + ∆𝐈𝐝(𝐗𝐪 −
𝐗𝐝′ )𝐈𝐪𝟎 (31)
∆𝐕𝐭𝐝 = 𝐗𝐪∆𝐈𝐪 , ∆𝐕𝐭𝐪 = ∆𝐄𝐪′ − 𝐗𝐝
′ ∆𝐈𝐝 (32)
Where:
(33)
(34)
(35)
BcδδBcbEcδδ
Ecedc9q87dc
ΔδKΔmKΔδK
ΔmKΔVKEΔKΔδKΔV
(36)
B
B
E
E
cdbcbcdece
m
m
KKKK
vdbA
1
AvbA
1
AvdeA
1
A5A
1
A
qdb
1
doqb
1
doqde
1
doqe
1
do
pdb
1
pb
1
pde
1
pe
1
KKTKKTKKTKKT
KTKTKTKT
KMKMKMKM
0000 (37)
Detailed values calculation of K coefficients can be find in [2]. As we can see the above equation is the standard
form of linear system as below:
∆�� = 𝑨∆𝑿 + 𝑩∆𝑼 (38)
This matrices equation is suitable for classical linear
control and numerical solving the system equations as
well as controllability analysis such as Eigen values
related techniques.
7. System simulation
7.1. Implementation algorithm
We have applied this simulation method to several
power systems and we bring results of two of them here,
first one is 39 bus new England power network and
second one is IEEE 9 bus test system. For small signal
analysis the sampling time selected 0.1 msec thus
frequency of two UPFC inverters parameters updating is
10 khz which have compliance with nowadays switches
speeds. In both two cases a power system Stabilizer
(PSS) has used only for the generator which is installed
on the slack bus. This study can be briefly described in
the following flowchart:
i. Reading power system and UPFC data;
ii. Load flow running with considering practical
limits and obtaining steady state operating point
data of system and machines;
iii. Using operating point data to calculate UPFC
parameters;
iv. Running load flow with UPFC installed
regarding constraints and then obtaining new
parameters values of system, machines and UPFC;
v. Computing linearized equations format of
whole system using previous step data and system
Eigen values;
vi. Calculating POD optimized parameters using
PSO;
vii. Small signal equations solving with all four
adjusted PI basic controllers of UPFC and adjusting
UPFC four parameters in every each iteration in all
time intervals consisting before, during and after
fault occurrence;
viii. Considering practical constraints of lines and
UPFC ratings in each every iteration and modifying
UPFC parameters and obtained powers if needed;
ix. Modifying POD parameters to new optimized
values if needed in some iteration.
7.2. The 39-Bus Power system simulation results
Figure 4 shows the studied power system which is 10-
machine 39-bus New England network. In this study, a
MATLAB program to simulate the model has used. The
result of load flow implementation is used to find UPFC
placement to improve voltage profile and load flow of
power system.
BpdbBpbEpde
Epedcpdq21e
ΔδKΔmKΔδK
ΔmKΔVKEΔKΔδKΔT
BqdbBqbEqde
Eqedcqdq34q
ΔδKΔmKΔδK
ΔmKΔVKEΔKΔδKΔE
BvdbBvbEvde
Evedcvdq65t
ΔδKΔmKΔδK
ΔmKΔVKEΔKΔδKΔV
DCDCVV
fd
q
987
vdA
1
A
1
A6A
1
A5A
1
A
qd
1
do
1
do3
1
do4
1
do
pd
1
2
11
1
1
fd
q
ΔE
EΔ
Δω
Δδ
K0K0K
KΚTΤKKT0KKΤ
ΚTΤKT0ΚΤ
ΚΜ0KMDMΚΜ
000I0
EΔ
EΔ
ωΔ
δΔ 0
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
260
Fig. 3. Flowchart of simulation and optimization
Fig. 4. New England power system network schematic
single line
Within load flow solution the thermal limits of lines
capacity considered. After UPFC insertion in power
network the load flow executed again. It is shown that
when UPFC is installed between two buses in the system,
the active and reactive power loses are reduced. It is also
has shown that not only the power losses are reduced, the
voltage profile of the every bus improved after
incorporate UPFC too.
For small signal and dynamic stability study we used
UPFC dynamic model and interfacing with power system
as described in 6.2. Linearized model of the multi-
machine power system consisting in UPFC, has used to
small signal analysis and damping oscillations studies.
The power rating limits of UPFC and lines capacity limits
have taken in to account during analysis. All four basic
controller of UPFC considered. Eigen values and
damping ratios of the linearized system derived and
based on these values the PSO algorithm have used to
optimize damping oscillations controller. Figure 5(a)
demonstrates the Eigen values of the system with and
without UPFC in complex plane. We can see some of
Eigen values have a little more negative real part and
smaller imaginary part. Figure 5(b) shows one machines
speed and load angle before and after inserting UPFC
which demonstrated the stabilizing impact of UPFC after
earth fault occurrence.
(a)
(b)
Fig. 5. System with and without UPFC
comparison.(a)Eigen values.(b) machine no. 5 speed
variation with and without UPFC in earth fault
occurrence
To investigate enhancement of power system stability
by a UPFC, we have studied results and responses of
these two different scenarios: (1) three phase earth fault
on the one of existing lines and (2) opening the circuit in
one of the existing lines of power system. Removing time
of both faults has selected enough small so we can use
small signal analysis and investigate dynamic stability.
But in scenario 2 it may that in several conditions due to
changing in network topology have changing in steady
state operating point, and then previous parameters can’t
be used thus should calculate new operating parameters
of UPFC and system variables values.
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
261
For UPFC performance analyse, two cases have
considered and applied to simulated system: (i) the
practical constraints not applied; (ii) the practical
constraints taken in to account.
7.2.1. Scenario 1: Short circuit fault
Three phase earth fault applied to line between bus 3
and 4 at 0.1 sec of simulation beginning and its duration
to clear is less than 0.1 sec which is enough short for
small signal analysis. Figure 6(a), shows the variation of
four UPFC control parameters i.e. 𝒎𝑬 , 𝒎𝑩 , 𝜹𝑬 and
𝜹𝑩 and 6(b) four output linearized control variables:
UPFC dc voltage, the UPFC installed or sending bus
voltage magnitude, active and reactive power flow in
UPFC installed line and 6(c) voltage of the bus which
UPFC installed and 6(d) voltage of the bus which fault
occurred in it and 6(e) active and 6(f) reactive power flow
which have controlled by UPFC and 6(g) four machines
speed variations before using UPFC and 6(h) same
machines speed variations after using UPFC with three
phase earth fault applied without considering practical
constraints and limits.
(a)
(b)
(c)
(d)
(e)
(f)
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
262
(g)
(h)
Fig.6. Damping effect of UPFC in three phase earth
fault without considering practical limits in 39-Bus
system.
Figure 7 shows the same parameters of figure 6 but
with considering practical constraints and limits
respectively.
(a)
(b)
(c)
(d)
(e)
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
263
(f)
(g)
Fig. 7. Damping effect of UPFC in three phase earth
fault with considering practical limits in 39-Bus system.
Figure 8 shows the effect of considering practical
constraints in 39-Bus system. 8(a) demonstrate Active
and reactive power flow in line which UPFC installed
comparing result without considering constraint and with
considering constraints and in 8(b) one machine speed
and 8(c) one machine load angle in two condition , one
with considering constraints and another without
considering constraints. As we can see in two figures 6
and 7 and with compare them, and with more contrast in
figure 8, it is observable that after fault the variation of
active and reactive power which UPFC should control is
too much and in real system we not permitted to have this
rating with multiple time of base power rating. Because
of applying these limit there are disturbances in UPFC
controlled parameters but the results are more acceptable.
And these limits consideration have not deteriorated
stability and damping of oscillations and more or less
lead to more stability.
7.2.2. Scenario 2: switch opening fault
The line switch between bus 13 and 14 has opened at
0.1 sec of simulation beginning and its duration is 0.1
sec too.
(a)
(b)
(c)
Fig. 8. Effect of practical constraints consideration in
39-Bus system
Figure 8 shows 9(a) voltage of the bus which UPFC
installed and 9(b) voltage of the bus which the line which
have opened had showed in 9(c) active and 9(d) reactive
power flow which have controlled by UPFC and 9(e) 4
machines speed variation while UPFC not used and 9(f)
four machines speed variations with UPFC and limits
applied. As we can see in this scenario the operating point
has changed. Then with controlled damping due to UPFC
effect, parameters have changed to new values without
instability.
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
264
(a)
(b)
(c)
7.3. The 9-Bus Power system simulation results
Figure 10 shows the 9 bus system with UPFC with
short circuit fault applying in line between bus 2 and 3 in
.1 sec after simulation and its duration is 0.1 sec. we
compared the results of system response while
considering practical constraints with them while hasn’t
considering those constraints.. As we can see in the figure
10(a), the practical constraints consideration leads to
better and faster response of UPFC power flow.
(d)
(e)
(f)
Fig. 9. Damping Effect of UPFC in line switch opening
with considering practical limits in 39-Bus system.
In Figure 10(b) and (c) the speed and load angle of one
of the machines have shown. And we can see that the
practical limits consideration leads to different variation
in speed and load angle of machines and has little
affected the damping curve of them but hasn’t deteriorate
stability of machines and system.
Tabriz Journal of Electrical Engineering (TJEE), vol. 51, no. 2, summer 2021 Serial no. 96
265
(a)
(b)
(c)
Fig. 10. Effect of practical constraints consideration in
9-Bus system
8. Conclusions
In this study, the power system with UPFC and its
main and damping controls has modeled. All of four
basic control and POD controller used simultaneously
and sometimes we found the conflict between them
during tuning of them but with compromising between
them the conflict have acceptably reduced. We applied
line transferring capacity thermal limits and UPFC active
and reactive power ratings during load flow and small
signal analyses. Applying practical constraints and limits
affected the four parameters of UPFC adjusted values, so
we have deviation in controlled parameters in particular
active and reactive power damping trends. It is important
that we hadn’t any unsafe over/under shoots in electrical
parameters which in real system not allowed and can’t
realize due to technical and economic aspects. The time
of damping power and speed oscillations and settling
may be little more while we applied those limits. In both
two scenario the limits delayed the time of damping
oscillations and omitted undesirable values, but in case
of three-phase earth fault this effects is more considerable
in compare with line opening. These limitation applying
didn’t deteriorate stability and Eigen values. This simple
method even in some changing topologies leads to
acceptable result in damping oscillation and stability
analyses.
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Appendix:
UPFC used Data:
In IEEE 9-Bus system: UPFC Rating=0.5 pu, xE=0.05
pu, xB=0.05 pu, Cdc=1 pu, Sb=100MW.
In 39-bus New England network: UPFC Rating=1.9 pu,
xE= 0.0725 pu, xB=0.0725 pu, CDC=1 pu, Sb=100MW.